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Maths-

SAT

Easy

Question

x²-12x + 23 = 0
Which of the following is a solution to the given equation?

$- 12 + \sqrt{11}$
$12 + \sqrt{11}$
$- 6 + \sqrt{13}$
$6 + \sqrt{13}$

The correct answer is: $6 plus square root of 13$

Given x² – 12x + 23 = 0
$equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$
a = 1, b = -12, c = 23
$equals fraction numerator 12 plus-or-minus square root of left parenthesis negative 12 right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 23 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction$
$equals fraction numerator 12 plus-or-minus square root of 144 minus 92 end root over denominator 2 end fraction$
$equals fraction numerator 12 plus-or-minus square root of 52 over denominator 2 end fraction$
$equals fraction numerator 12 plus-or-minus square root of 4 cross times 13 end root over denominator 2 end fraction equals fraction numerator 12 plus-or-minus 2 square root of 13 over denominator 2 end fraction$
$equals 2 open parentheses fraction numerator 6 plus-or-minus square root of 13 over denominator 2 end fraction close parentheses equals 6 plus-or-minus square root of 13$

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